High-throughput techniques are producing large-scale high-dimensional (e.g., 4D with genes vs timepoints vs conditions vs tissues) genome-wide gene expression data. This induces increasing demands for effective methods for partitioning the data into biologically relevant groups. Current clustering and co-clustering approaches have limitations, which may be very time consuming and work for only low-dimensional expression datasets. In this work, we introduce a new notion of "co-identification", which allows systematical identification of genes participating different functional groups under different conditions or different development stages. The key contribution of our work is to build a unified computational framework of co-identification that enables clustering to be high-dimensional and adaptive. Our framework is based upon a generic optimization model and a general optimization method termed Maximum Block Improvement. Testing results on yeast and Arabidopsis expression data are presented to demonstrate high efficiency of our approach and its effectiveness.